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Chapter 6: Functions

Chapter 6: Functions. Outline Introduction Function Definitions Function Prototypes Function Name by Identifier __func__ Recursive Functions Header Files Type Generic Functions Function Files Sample Problem Indirect Recursive Functions

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Chapter 6: Functions

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  1. Chapter 6: Functions Outline Introduction Function Definitions Function Prototypes Function Name by Identifier __func__ Recursive Functions Header Files Type Generic Functions Function Files Sample Problem Indirect Recursive Functions Variable Number Arguments in Functions Extensions in Ch Nested Functions

  2. Introduction • A C program is generally formed by a set of functions. These functions subsequently consist of many programming statements. • By using functions, a large task can be broken down into smaller ones. • Functions are important because of their reusability. That is, users can develop an application program based upon what others have done. They do not have to start from scratch.

  3. Function Definitions • A function can be defined in the form of return_type function_name(argument declaration) { statements } Example: int addition(int a, int b) { int s; s = a + b; return s; } int main() { int sum; sum = addition(3, 4); printf(“sum = %d\n”, sum); return 0; }

  4. The return type can be any valid type specifier. • The return statement can be used to return a value from the called function to the calling function as in return expression; If necessary, the expression will be converted to the return type of the function. However, if the expression cannot be converted to the return type of the function according to the built-in data type conversion rules implicitly, it is a syntax error. Example: int func(void) { double d; d = 4.6; return d; // OK: C type conversion, return 4 }

  5. If the return type is not void, a return statement is necessary at the end of the function in C99. Otherwise, the default zero will be used as the return value and a warning message will be produced by the system in C90 and Ch. • A calling function can freely ignore the return value. Example: int func(int i){ return i+1; // the same as ‘return (i+1);’ } int main() { int j; j = func(4); func(5); // ignore the return value return 0; }

  6. If the return type is void, the return statement is optional. However, no expression should follow return; otherwise, it is a syntax error. Example: void func(int i) { if(i == 3) { printf("i is equal to 3 \n"); return i; // ERROR: return int } else if(i > 3) { printf("i is not equal to 3 \n"); return; // OK } i = -1; // return not necessary since return type is void } int main(){ func(2); return 0; }

  7. The data type of an actual argument of the calling function can be different from that of the formal argument of the called function as long as they are compatible. The value of an actual argument will be converted to the data type of its formal definition according to the built-in data conversion rules implicitly at the function interface stage. Example: int func1(int i) { // argument type is int return 2*i; } int main(){ func1(5); // OK func1(5.0); // OK, 5.0 converted to 5 return 0; }

  8. Sample Problem: The system in Figure1 (a) consists of a single body with mass m moving on a horizontal surface. An external force p acts on the body. The coefficient of kinetic friction between body and horizontal surface is  . The freebody diagram for the system is shown in Figure1 (b). Figure1: The system diagram and FBD of a sample problem

  9. The nomenclature related to the modeling of the system is listed below. m -- mass of the body x -- position of the bodyv -- velocity of the bodya -- acceleration of the bodyg -- gravitational acceleration -- friction coefficient f -- friction force N -- normal force Equation of motion: The equation of the motion of the system can be derived based on the Newton's second law. N = mg (1) f =  N (2) p-f = ma (3) From equation (1), (2) and (3), the formula for calculating the acceleration of the rigid body can be derived as follows. a = (p- mg)/m (4)

  10. Problem Statement: For the system shown in Figure1(a), given m = 5 kg, g = 9.81 m/s2,  = 0.2. The external force p is expressed as a function of time t, p(t) = 4(t-3)+20 when t >= 0 write a program to calculate the acceleration a when t = 2 seconds. Solve the above problem using two different programs with the features specified below. • Use a function to calculate the external force. • Use a function with multiple arguments to calculate the acceleration.

  11. Program 1: Use a function to calculate the external force. /* File: accelfun.c */ #include <stdio.h> #define M_G 9.81 double force(double t) { double p; p = 4*(t-3)+20; return p; } int main() { double a, mu, m, p, t; mu = 0.2; m = 5.0; t = 2.0; p = force(t); a = (p-mu*m*M_G)/m; printf("Acceleration a = %f (m/s^2)\n", a); return 0; } Output: Acceleration a = 1.238000 (m/s^2)

  12. Program 2: Use functions with multiple arguments. /* File: accelfunm.c */ #include <stdio.h> #define M_G 9.81 double force(double t) { double p; p = 4*(t-3)+20; return p; } double accel(double t, double mu, double m) { double a, p; p = force(t); a = (p-mu*m*M_G)/m; return a; } int main() { double a, mu, m, t; mu = 0.2; m = 5; t = 2; a = accel(t, mu, m); printf("Acceleration a = %f\n (m/s^2)", a); return 0; }

  13. Function Prototypes • A function prototype is a declaration of a function that declares the return type and types of its parameters. For example, double force(double t); double accel(double t, double mu, double m); • A function prototype contains no function definition. • A function prototype can be declared at any lexical level, before and after its function definition. • If the function is called before it is defined, int is assumed to be the return type of the function. Therefore, a function prototype is required if the return type of the function is not int and the function is called before its definition is processed, or if the function definition is located in a different file or in a library.

  14. Problem Statement: For the system shown in Figure1(a), given m = 5 kg, g = 9.81 m/s2,  = 0.2. The external force p is expressed as a function of time t, p(t) = 4(t-3)+20 when t >= 0 write a program to calculate the acceleration a when t = 2 seconds. Solve the above problem using the features specified below. • Use a function with multiple arguments to calculate the acceleration. The program lists function main() before other functions.

  15. Program 3: Use function prototypes. /* File: accelprot.c */ #include <stdio.h> #define M_G 9.81 double force(double t); double accel(double t, double mu, double m); int main() { double a, mu, m, t; mu = 0.2; m = 5.0; t = 2.0; a = accel(t, mu, m); printf("Acceleration a = %f (m/s^2)\n", a); return 0; } double force(double t) { double p; p = 4*(t-3)+20; return p; } double accel(double t, double mu, double m) { double a, p; p = force(t); a = (p-mu*m*M_G)/m; return a; }

  16. Parameter names must appear in function definitions, but the parameter names for arguments of function prototypes does not have to be included. For example, the following two function prototypes are the same. double accel(double, double, double); double accel(double t, double mu, double m);

  17. Function prototype int func(); has different meaning in the C and C++. • In C++, it means that function func() has no arguments. • In C, it means that function func() could have any number of arguments. The number of arguments and the data types of the arguments of the function depend on the function definition. For example, the definition of the func could be int func(int i) {} // func has one argument or int func(int i, int j) {} // func has two arguments or int func(double x, double y, int i) {} // func has three arguments

  18. Standard C Header Files and Libraries • Header files typically contain function prototypes for performing operations that are related to one another. They may also include macros and type definitions required by some of the functions. For example, header file math.h contains the function prototypes extern double sin(double x); extern double exp(double x); for mathematical functions sin(x) and ex. The type qualifier extern for functions defined in a library or other module. • Each C compiler and interpreter has its own header files for the standard C libraries. For example, these header files in Ch are located in the directory C:/Ch/include in Windows and /usr/local/ch/include in Unix by default.

  19. Some Standard C Header Files

  20. Type Generic Functions • A generic function is a built-in system function. • Most generic functions are polymorphic. • When a generic function such as sin() is explicitly called, the built-in system function is used even if the user has redefined the function. This allows for the argument of the sin() to be any valid data type. • To use type generic mathematical functions in C99, the header file tgmath.h shall be included.

  21. Standard C functions • A reference manual with detailed description for each function in the standard C libraries is available in CHHOME/docs/chref.pdf, such as C:/ch/docs/chref.pdf. • Demonstration programs for each function in the standard C libraries are available in CHHOME/demos/lib/libc/, such as C:/Ch/demos/lib/libc/, directory

  22. A Mathematical Formula with a Single Variable Calculate function sinc(x) = sin(x)/x from -10 <= x <= 10 with a step size 5. Modify program forsinc.c. Generate data points (x, y) for x in the range x0 <= x <= xf with step size xstep linearly. The number of points n = (xf – x0)/xstep + 1; Each data point can be calculated by for(i = 0; i <n; i++) { x = x0 + i*xstep; y = f(x); }

  23. /* File: sinc.c */ #include <stdio.h> /* for printf() */ #include <math.h> /* for sin() and fabs() */ #include <float.h> /* for FLT_EPSILON */ double sinc(double x) { double retval; if(fabs(x) < FLT_EPSILON) retval = 0.0; else retval = sin(x)/x; return retval; } int main() { double x, x0, xf, xstep, result; int i, n; printf(" x sinc(x)\n"); printf(" ---------------\n"); x0 = -10.0; /* initial value */ xf = 10.0; /* final value */ xstep = 5.0; /* step size */ n = (xf - x0)/xstep + 1; /* num of points */ for(i = 0; i < n; i++) { x = x0 + i*xstep; /* value x */ result = sinc(x); printf("%8.4f %8.4f\n", x, result); } return 0; } Output: x sinc(x) ---------------- -10.0000 -0.0544 -5.0000 -0.1918 0.0000 0.0000 5.0000 -0.1918 10.0000 -0.0544

  24. Calculating Polynomial Functions • Note: • x2 can be calculated using either x*x or exponential function pow(x,2) declared in header file math.h with pow(x,y) for xy . The expression x*x is faster than pow(x,2).

  25. 2D Plotting Function • fplotxy() is a high-level 2D plotting function. • The prototype for function fplotxy() is as follow. • int fplotxy(double func(double), • double x0, double xf, int num, • char *title, char *xlabel, char *ylabel); • The argument func is a pointer to function for a function to be plotted in the range from x0 to xf with the num of points. The remaining arguments are for title, label for x-axis, and label for y-axis. • The first argument of the function fplotxy() is a function with the function • prototype of • double func(double x); • The function fplotxy() can be called as follows. • fplotxy(func,x0,xf,num,title,xlabel,ylabel);

  26. Plot function sinc(x) = sin(x)/x from -10 <= x <= 10 with 80 points. /* File: sinc_fplotxy.cpp */ #include <math.h> #include <chplot.h> double sinc(double x) { double retval; retval = sin(x)/x; return retval; } int main() { double x0 = -10.0, xf = 10.0; int num = 80; fplotxy(sinc, x0, xf, num, "function sinc()", "x", “sinc(x)"); return 0; }

  27. Output of the program:

  28. Demo 1. Run program sinc_fplotxy.c in ChIDE. 2. Copy the plot into the Clipboard. a. Click upper left icon of the displayed plot, b. click Options, c. click Copy to Clipboard 3. Open Word, paste the copied plot into it.

  29. Copy a plot into clipboard to be pasted in a Word file

  30. Problem Statement For the system shown in Figure1(a), given m = 5 kg, g = 9.81 m/s2,  = 0.2. The external force p is expressed as a function of time t, p(t) = 4 sin(t-3)+20 when t >= 0 (1) Write a program to plot the accelerations a when t = 0 to t = 10 with 11 points. (2) Write a program to plot the accelerations a during t = 0 to t = 10 with 100 points.

  31. int main() { double t0 = 0, tf = 10; int num = 11; fplotxy(accel, t0, tf, num, "Acceleration Plot", "time (s)", "accel (m/s^2)"); return 0; } /* File: accelsinplot.cpp */ #include <stdio.h> #include <math.h> #include <chplot.h> #define M_G 9.81 double force(double t) { double p; p = 4*sin(t-3)+20; return p; } double accel(double t) { double mu, m, a, p; mu = 0.2; m = 5; p = force(t); a = (p-mu*m*M_G)/m; return a; }

  32. Output of the program with num = 11:

  33. Output of the program with num = 100:

  34. Using the plotting class CPlot to plot multiple functions in the same plot. fplotxy(func, x0, xf, num, title. xlabel, ylabel); has the same effect as CPlot plot; plot.title(title); plot.label(PLOT_AXIS_X, xlabel); plot.label(PLOT_AXIS_Y, ylabel); plot.func2D(x0, xf, num, func); plot.plotting() CPlot is a data type defined in header file chplot.h. Others are member functions to handle the associated data for the object plot.

  35. Plot two acceleration curves in a single plot Member function call plot.legend(“string”,num); adds a legend of string for the data set num. Numbering of data set starts with zero. /* File: accelfunc2D.cpp */ #include <stdio.h> #include <math.h> #include <chplot.h> #define M_G 9.81 double accel(double t) { double mu, m, a, p; mu = 0.2; m = 5; p = 4*sin(t-3)+20; a = (p-mu*m*M_G)/m; return a; } int main() { double t0 = 0, tf = 10; int num1 = 11, num2 = 100; CPlot plot; plot.title("Acceleration Plot"); plot.label(PLOT_AXIS_X, "time (s)"); plot.label(PLOT_AXIS_Y, "accel (m/s^2)"); plot.func2D(t0, tf, num1, accel); plot.legend("11 points", 0); plot.func2D(t0, tf, num2, accel); plot.legend("100 points", 1); plot.plotting(); return 0; }

  36. Output of the program

  37. A Mathematical Formula with Multiple Variables Calculate function for x from -10 <= x <= 10 with a step size 10 and y from -10 <= y <= 10 with a step size of 10.

  38. /* File: sinr.c */ #include <stdio.h> #include <math.h> double sinr(double x, double y) { double retval, r; r = sqrt(x*x + y*y); retval = sin(r)/r; return retval; } int main() { double x, x0, xf, xstep, y, y0, yf, ystep, result; int i, j, nx, ny; printf(" x y sinr(x,y)\n"); printf(" -----------------------------\n"); x0 = -10.0; xf = 10.0; xstep = 10.0; nx = (xf - x0)/xstep + 1; /* num of points for x */

  39. y0 = -10.0; yf = 10.0; ystep = 10.0; ny = (yf - y0)/ystep + 1; /* num of points for y */ for(i = 0; i < nx; i++) { x = x0 + i*xstep; /* caclulate value for x */ for(j = 0; j <ny; j++) { y = y0 + j*ystep; /* calculate value for y */ result = sinr(x, y); printf("%10.4f %10.4f %8.4f\n", x, y, result); } } return 0; } x y sinr(x,y) ----------------------------- -10.0000 -10.0000 0.0707 -10.0000 0.0000 -0.0544 -10.0000 10.0000 0.0707 0.0000 -10.0000 -0.0544 0.0000 0.0000 NaN 0.0000 10.0000 -0.0544 10.0000 -10.0000 0.0707 10.0000 0.0000 -0.0544 10.0000 10.0000 0.0707 Output: sin(0)/0 is NaN

  40. 3D Plotting Function • fplotxyz() is a plotting function for functions with two variables. • The prototype for function fplotxyz() is as follow. • int fplotxyz(double func(double, double), • double x0, double xf, double y0, yf, • int numx, int numy, char *title, • char *xlabel, char *ylabel, char *zlabel); • The argument func is a pointer to function for a function to be plotted for x-coordinates in the range from x0 to xf with the numx of points and for the y-coordinates in the range from y0 to yf with the numy of points The remaining arguments are for title, labels for x-axis, y-axis, and z-axis. • The first argument of the function fplotxyz() is a function with the function prototype of • double func(double x, double y); • The function fplotxyz() can be called as follows. • fplotxy(func,x0,xf,y0,yf, numx,numy, • title,xlabel,ylabel,zlabel);

  41. for x from -10 <= x <= 10 with 80 points and y from -10 <= y <= 10 with 100 points. /* File: hat.cpp */ #include <math.h> #include <chplot.h> double sinr(double x, double y) { double retval, r; r = sqrt(x*x + y*y); retval = sin(r)/r; return retval; } int main() { double x0 = -10.0, xf = 10.0, y0 = -10.0, yf = 10.0; int numx = 80, numy = 100; fplotxyz(sinr, x0, xf, y0, yf, numx, numy, "function sinr(x, y)", "x", "y", “sinr(x, y)"); return 0; } Plot function

  42. Output of the program:

  43. Recursive Functions • Functions may be used recursively. This means that a function can call itself directly. • When a function calls itself recursively, each function call will have a new set of local variables. • Recursive functions usually contain conditional statements, such as if-else, to allow exit of the function and return control to the calling function. • A function may also call itself indirectly.

  44. Example: Calculating a factorial 5! using a function with a for-loop. The factorial n! is defined as n*(n-1)! Output: 0! = 1 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 /* File: factorloop.c */ #include <stdio.h> unsigned int factorial(int n); int main() { int i; for(i=0; i<=5; i++) printf("%d! = %d\n", i, factorial(i)); return 0; } unsigned int factorial(int n) { unsigned int i, f; for(i=1, f=1; i<=n; i++) { f *= i; } return f; }

  45. Example: Calculating a factorial 5! using a recursive function. /* File: factorrecursive.c */ #include <stdio.h> unsigned int factorial(int n); int main() { int i; for(i=0; i<=5; i++) printf("%d! = %d\n", i, factorial(i)); return 0; } unsigned int factorial(int n) { if(n <= 1) { return 1; } else { return n*factorial(n-1); } } Output: 0! = 1 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120

  46. int main(){ int f = factorial(2); } int main( ){ int f = 2; } int factorial(int n){ // n=2 if(n<=1) return 1; else return n*factorial(n-1); } int factorial(int n){ // n=2 if(n<=1) return 1; else return 2*factorial(1); } int factorial(int n){ // n=2 if(n<=1) return 1; else return 2*1; } int factorial(int n){ // n=1 if(n<=1) return 1; else return n*factorial(n-1); }

  47. Predefined Identifier __func__ • The data type for __func__ is char*. • Inside a function, it is a pointer to string obtaining the function name. Example: /* File: funcname.c */ #include <stdio.h> void funcname(void) { printf("The function is %s\n", __func__); } int main() { funcname(); return 0; } Output: The function is funcname

  48. Function Files • A function file in Ch is a file that contains only one function definition and has the file extension .chf. • The names of the function file and function definition inside the function file must be the same. • The functions defined using function files are treated as if they were the system built-in functions in a Ch programming environment. • It is a good practice to contain only one function in a function file. • A function is searched based on the paths, separated by semicolon ‘;’, in the system variable _fpath. By default, it contains “CHHOME/lib/libc;CHHOME/lib/libch;CHHOME/lib/libopt;CHHOME/lib/libch/numeric;”. • Add a directory for the function file _fpath = stradd(_fpath, “/home/harry/eme5;”); in _chrc for Windows and .chrc in Linux in the user’s home directory.

  49. Example: /* File: addition.chf */ int addition(int a, int b) { int c; c = a + b; return c;} /* program.ch using function file addition.chf. */ int main() { int a, b, c; a = 2; b = 3; c = addition(a, b); printf(“c = %d\n", c); return 0; }

  50. A function in function file can be invoked interactively in command shell. For example, C:/Ch> int i = 9 C:/Ch> i = addition(3, i) 12 C:/Ch>

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